This problem is an extension of problem 12.1 from Lomax & Hahs-Vaughn, 3rd ed.

A researcher has randomly assigned 8 participants to five different strategy training sessions to help people cope with stress at work.  The researcher believes that more effective stress-coping strategies should result in higher job-satisfaction ratings.  Thus, after the participants undergo the training session, she asks them to complete a survey 6 months later to assess their satisfaction with their jobs.  At first glance, she has no reason to reject the assumption that the ratings from the different treatments are not independent and normally distributed with equal variance.  Of course, the overarching question is whether or not the different treatments have any relationship with overall job-satisfaction ratings.

Group-1	Group-2	Group-3	Group-4	Group-5
78.6	80.1	87.6	85.1	75.7
55.5	75.4	93.8	85.6	76.9
74.2	80.4	88.7	82.6	81.9
75.1	78.2	86.4	90.2	86.6
70.6	78.9	88.8	91.9	85.6
65.3	77.8	78.3	93.6	75.4
71.7	78.8	74.9	97	85
81.6	84.7	86.1	97.2	87.4

Use SPSS (or another statistical software package) to conduct a one-factor ANOVA to determine if the group means are equal using $\displaystyle \alpha={0.05}$.  Though not specifically assessed here, you are encouraged to also test the assumptions, plot the group means, and interpret the results (e.g., if there was an effect, what was the magnitude).

ANOVA summary table (report all values accurate to 3 decimal places):

Source	SS	df	MS
Group
Error

ANOVA summary statistics:
F-ratio =     (report accurate to 3 decimal places)
Conclusion from the omnibus test:

In addition, based on subtle similarities or differences between the training sessions, the researcher wants to examine a group of orthogonal contrasts:

Contrast	$\displaystyle {c}_{{1}}$	$\displaystyle {c}_{{2}}$	$\displaystyle {c}_{{3}}$	$\displaystyle {c}_{{4}}$	$\displaystyle {c}_{{5}}$
$\displaystyle \psi_{{1}}$	$\displaystyle -{3}$	$\displaystyle {2}$	$\displaystyle {2}$	$\displaystyle -{3}$	$\displaystyle {2}$
$\displaystyle \psi_{{2}}$	$\displaystyle {0}$	$\displaystyle {1}$	$\displaystyle {1}$	$\displaystyle {0}$	$\displaystyle -{2}$
$\displaystyle \psi_{{3}}$	$\displaystyle {1}$	$\displaystyle {0}$	$\displaystyle {0}$	$\displaystyle -{1}$	$\displaystyle {0}$
$\displaystyle \psi_{{4}}$	$\displaystyle {0}$	$\displaystyle {1}$	$\displaystyle -{1}$	$\displaystyle {0}$	$\displaystyle {0}$

Questions for reflection:  What is actually being tested with these contrasts?  In particular, for each contrast, which combined group averages are being compared to what?  Finally, confirm that each contrast is valid and that each pair is orthogonal.

The researcher prefers to control for experiment-wise significance ($\displaystyle \alpha_{{\text{fw}}}={0.05}$), and decides to use the Scheffé test.  This requires finding the critical value for these contrasts (report to 3 decimal places):
$\displaystyle {t}_{{\text{c.v.}}}=$

Calculate the t-ratio for each contrast (report all values to 3 decimal places):
    Contrast 1:
          $\displaystyle \psi_{{1}}=$
          $\displaystyle {t}_{{1}}=$
    Contrast 2:
          $\displaystyle \psi_{{2}}=$
          $\displaystyle {t}_{{2}}=$
    Contrast 3:
          $\displaystyle \psi_{{3}}=$
          $\displaystyle {t}_{{3}}=$
    Contrast 4:
          $\displaystyle \psi_{{4}}=$
          $\displaystyle {t}_{{4}}=$

Using the t-ratios and the critical value, which contrasts were statistically significantly different from zero?